NN-based Control Methods for Dynamic Systems

Reference Tracking Neural Network Controller for Dynamic Systems

The controller utilizes Neural Networks to control a nonlinear dynamic system by tracking a given reference signal. The main goal is to minimize the error between the system output and the desired reference trajectory.

Block Diagram

Components Description

1. Reference Model:

   • The reference model is defined by the transfer function: $$G_m(s)=\frac{K}{\frac{1}{{\omega }_n^2}{s}^2+\frac{2\xi }{{\omega }_n}s+1}$$
   • Generates the desired reference signal.
   • Uses the reference input which is given by: $$r(k)=\sin \left(\frac{2\pi k}{25}\right)+\sin \left(\frac{2\pi k}{10}\right)$$

2. Dynamic System:

   • The nonlinear dynamic system is represented by: $$y(k+1)=\frac{y(k)y(k-1)u(k)+u^3(k)+0.5y(k-1)}{1+y^2(k)+y^2(k-1)}$$

3. NN Controller:

   • Adjusts the control input to minimize the tracking error.
   • Utilizes gradients and parameters of the RBF NN model to update the control signal.

Result

Reference

[1] Slema, S., Errachdi, A., & Benrejeb, M. (2018, March). A radial basis function neural network model reference adaptive controller for nonlinear systems. In 2018 15th International Multi-Conference on Systems, Signals & Devices (SSD) (pp. 958-964). IEEE.

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